if 5tan⁡ϕ=tan⁡θ then the maximum value of 5tan2⁡(θ−ϕ) is

if 5tanϕ=tanθ then the maximum value of 5tan2(θϕ) is

  1. A

    1

  2. B

    4

  3. C

    6

  4. D

    9

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    Solution:

    t=tanϕ,tan(θϕ)=5tt1+5t2=4t1+5t2

    5tan2(θϕ)=80t21+5t22=801t+5t280(25)2=4

    sinceA.M G.M.

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